Journal of the ACM (JACM)
Linear lists and priority queues as balanced binary trees
Linear lists and priority queues as balanced binary trees
An O(pn2) algorithm for the p -median and related problems on tree graphs
Operations Research Letters
Scalable fair reliable multicast using active services
IEEE Network: The Magazine of Global Internetworking
A new template for solving p-median problems for trees in sub-quadratic time
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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Content-Based Multicast is a type of multicast where the source sends a set of different classes of information and not all the subscribers in the multicast group need all the information. Use of filtering publish-subscribe agents on the intermediate nodes was suggested [5] to filter out the unnecessary information on the multicast tree. However, filters have their own drawbacks like processing delays and infrastructure cost. Hence, it is desired to place these filters most efficiently. An O(n2) dynamic programming algorithm was proposed to calculate the best locations for filters that would minimize overall delays in the network [6]. We propose an improvement of this algorithm which exploits the geometry of piecewise linear functions and fast merging of sorted lists, represented by height balanced search trees, to achieve O(n log n) time complexity. Also, we show an improvement of this algorithm which runs in O(n log h) time, where h is the height of the multicast tree. This problem is closely related to p-median and uncapacitated facility location over trees. Theoretically, this is an uncapacitated analogue of the p-inmedian problem on trees as defined in [9].